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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.analysis.integration;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math3.analysis.UnivariateFunction;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.analysis.integration.gauss.GaussIntegratorFactory;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.analysis.integration.gauss.GaussIntegrator;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.exception.MaxCountExceededException;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.exception.NotStrictlyPositiveException;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.exception.NumberIsTooSmallException;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.exception.TooManyEvaluationsException;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.26"></a>
<FONT color="green">027</FONT>    <a name="line.27"></a>
<FONT color="green">028</FONT>    /**<a name="line.28"></a>
<FONT color="green">029</FONT>     * This algorithm divides the integration interval into equally-sized<a name="line.29"></a>
<FONT color="green">030</FONT>     * sub-interval and on each of them performs a<a name="line.30"></a>
<FONT color="green">031</FONT>     * &lt;a href="http://mathworld.wolfram.com/Legendre-GaussQuadrature.html"&gt;<a name="line.31"></a>
<FONT color="green">032</FONT>     * Legendre-Gauss&lt;/a&gt; quadrature.<a name="line.32"></a>
<FONT color="green">033</FONT>     *<a name="line.33"></a>
<FONT color="green">034</FONT>     * @version $Id: IterativeLegendreGaussIntegrator.java 1416643 2012-12-03 19:37:14Z tn $<a name="line.34"></a>
<FONT color="green">035</FONT>     * @since 3.1<a name="line.35"></a>
<FONT color="green">036</FONT>     */<a name="line.36"></a>
<FONT color="green">037</FONT>    <a name="line.37"></a>
<FONT color="green">038</FONT>    public class IterativeLegendreGaussIntegrator<a name="line.38"></a>
<FONT color="green">039</FONT>        extends BaseAbstractUnivariateIntegrator {<a name="line.39"></a>
<FONT color="green">040</FONT>        /** Factory that computes the points and weights. */<a name="line.40"></a>
<FONT color="green">041</FONT>        private static final GaussIntegratorFactory FACTORY<a name="line.41"></a>
<FONT color="green">042</FONT>            = new GaussIntegratorFactory();<a name="line.42"></a>
<FONT color="green">043</FONT>        /** Number of integration points (per interval). */<a name="line.43"></a>
<FONT color="green">044</FONT>        private final int numberOfPoints;<a name="line.44"></a>
<FONT color="green">045</FONT>    <a name="line.45"></a>
<FONT color="green">046</FONT>        /**<a name="line.46"></a>
<FONT color="green">047</FONT>         * Builds an integrator with given accuracies and iterations counts.<a name="line.47"></a>
<FONT color="green">048</FONT>         *<a name="line.48"></a>
<FONT color="green">049</FONT>         * @param n Number of integration points.<a name="line.49"></a>
<FONT color="green">050</FONT>         * @param relativeAccuracy Relative accuracy of the result.<a name="line.50"></a>
<FONT color="green">051</FONT>         * @param absoluteAccuracy Absolute accuracy of the result.<a name="line.51"></a>
<FONT color="green">052</FONT>         * @param minimalIterationCount Minimum number of iterations.<a name="line.52"></a>
<FONT color="green">053</FONT>         * @param maximalIterationCount Maximum number of iterations.<a name="line.53"></a>
<FONT color="green">054</FONT>         * @throws NotStrictlyPositiveException if minimal number of iterations<a name="line.54"></a>
<FONT color="green">055</FONT>         * is not strictly positive.<a name="line.55"></a>
<FONT color="green">056</FONT>         * @throws NumberIsTooSmallException if maximal number of iterations<a name="line.56"></a>
<FONT color="green">057</FONT>         * is smaller than or equal to the minimal number of iterations.<a name="line.57"></a>
<FONT color="green">058</FONT>         */<a name="line.58"></a>
<FONT color="green">059</FONT>        public IterativeLegendreGaussIntegrator(final int n,<a name="line.59"></a>
<FONT color="green">060</FONT>                                                final double relativeAccuracy,<a name="line.60"></a>
<FONT color="green">061</FONT>                                                final double absoluteAccuracy,<a name="line.61"></a>
<FONT color="green">062</FONT>                                                final int minimalIterationCount,<a name="line.62"></a>
<FONT color="green">063</FONT>                                                final int maximalIterationCount)<a name="line.63"></a>
<FONT color="green">064</FONT>            throws NotStrictlyPositiveException, NumberIsTooSmallException {<a name="line.64"></a>
<FONT color="green">065</FONT>            super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);<a name="line.65"></a>
<FONT color="green">066</FONT>            numberOfPoints = n;<a name="line.66"></a>
<FONT color="green">067</FONT>        }<a name="line.67"></a>
<FONT color="green">068</FONT>    <a name="line.68"></a>
<FONT color="green">069</FONT>        /**<a name="line.69"></a>
<FONT color="green">070</FONT>         * Builds an integrator with given accuracies.<a name="line.70"></a>
<FONT color="green">071</FONT>         *<a name="line.71"></a>
<FONT color="green">072</FONT>         * @param n Number of integration points.<a name="line.72"></a>
<FONT color="green">073</FONT>         * @param relativeAccuracy Relative accuracy of the result.<a name="line.73"></a>
<FONT color="green">074</FONT>         * @param absoluteAccuracy Absolute accuracy of the result.<a name="line.74"></a>
<FONT color="green">075</FONT>         */<a name="line.75"></a>
<FONT color="green">076</FONT>        public IterativeLegendreGaussIntegrator(final int n,<a name="line.76"></a>
<FONT color="green">077</FONT>                                                final double relativeAccuracy,<a name="line.77"></a>
<FONT color="green">078</FONT>                                                final double absoluteAccuracy) {<a name="line.78"></a>
<FONT color="green">079</FONT>            this(n, relativeAccuracy, absoluteAccuracy,<a name="line.79"></a>
<FONT color="green">080</FONT>                 DEFAULT_MIN_ITERATIONS_COUNT, DEFAULT_MAX_ITERATIONS_COUNT);<a name="line.80"></a>
<FONT color="green">081</FONT>        }<a name="line.81"></a>
<FONT color="green">082</FONT>    <a name="line.82"></a>
<FONT color="green">083</FONT>        /**<a name="line.83"></a>
<FONT color="green">084</FONT>         * Builds an integrator with given iteration counts.<a name="line.84"></a>
<FONT color="green">085</FONT>         *<a name="line.85"></a>
<FONT color="green">086</FONT>         * @param n Number of integration points.<a name="line.86"></a>
<FONT color="green">087</FONT>         * @param minimalIterationCount Minimum number of iterations.<a name="line.87"></a>
<FONT color="green">088</FONT>         * @param maximalIterationCount Maximum number of iterations.<a name="line.88"></a>
<FONT color="green">089</FONT>         * @throws NotStrictlyPositiveException if minimal number of iterations<a name="line.89"></a>
<FONT color="green">090</FONT>         * is not strictly positive.<a name="line.90"></a>
<FONT color="green">091</FONT>         * @throws NumberIsTooSmallException if maximal number of iterations<a name="line.91"></a>
<FONT color="green">092</FONT>         * is smaller than or equal to the minimal number of iterations.<a name="line.92"></a>
<FONT color="green">093</FONT>         */<a name="line.93"></a>
<FONT color="green">094</FONT>        public IterativeLegendreGaussIntegrator(final int n,<a name="line.94"></a>
<FONT color="green">095</FONT>                                                final int minimalIterationCount,<a name="line.95"></a>
<FONT color="green">096</FONT>                                                final int maximalIterationCount) {<a name="line.96"></a>
<FONT color="green">097</FONT>            this(n, DEFAULT_RELATIVE_ACCURACY, DEFAULT_ABSOLUTE_ACCURACY,<a name="line.97"></a>
<FONT color="green">098</FONT>                 minimalIterationCount, maximalIterationCount);<a name="line.98"></a>
<FONT color="green">099</FONT>        }<a name="line.99"></a>
<FONT color="green">100</FONT>    <a name="line.100"></a>
<FONT color="green">101</FONT>        /** {@inheritDoc} */<a name="line.101"></a>
<FONT color="green">102</FONT>        @Override<a name="line.102"></a>
<FONT color="green">103</FONT>        protected double doIntegrate()<a name="line.103"></a>
<FONT color="green">104</FONT>            throws TooManyEvaluationsException, MaxCountExceededException {<a name="line.104"></a>
<FONT color="green">105</FONT>            // Compute first estimate with a single step.<a name="line.105"></a>
<FONT color="green">106</FONT>            double oldt = stage(1);<a name="line.106"></a>
<FONT color="green">107</FONT>    <a name="line.107"></a>
<FONT color="green">108</FONT>            int n = 2;<a name="line.108"></a>
<FONT color="green">109</FONT>            while (true) {<a name="line.109"></a>
<FONT color="green">110</FONT>                // Improve integral with a larger number of steps.<a name="line.110"></a>
<FONT color="green">111</FONT>                final double t = stage(n);<a name="line.111"></a>
<FONT color="green">112</FONT>    <a name="line.112"></a>
<FONT color="green">113</FONT>                // Estimate the error.<a name="line.113"></a>
<FONT color="green">114</FONT>                final double delta = FastMath.abs(t - oldt);<a name="line.114"></a>
<FONT color="green">115</FONT>                final double limit =<a name="line.115"></a>
<FONT color="green">116</FONT>                    FastMath.max(getAbsoluteAccuracy(),<a name="line.116"></a>
<FONT color="green">117</FONT>                                 getRelativeAccuracy() * (FastMath.abs(oldt) + FastMath.abs(t)) * 0.5);<a name="line.117"></a>
<FONT color="green">118</FONT>    <a name="line.118"></a>
<FONT color="green">119</FONT>                // check convergence<a name="line.119"></a>
<FONT color="green">120</FONT>                if (iterations.getCount() + 1 &gt;= getMinimalIterationCount() &amp;&amp;<a name="line.120"></a>
<FONT color="green">121</FONT>                    delta &lt;= limit) {<a name="line.121"></a>
<FONT color="green">122</FONT>                    return t;<a name="line.122"></a>
<FONT color="green">123</FONT>                }<a name="line.123"></a>
<FONT color="green">124</FONT>    <a name="line.124"></a>
<FONT color="green">125</FONT>                // Prepare next iteration.<a name="line.125"></a>
<FONT color="green">126</FONT>                final double ratio = FastMath.min(4, FastMath.pow(delta / limit, 0.5 / numberOfPoints));<a name="line.126"></a>
<FONT color="green">127</FONT>                n = FastMath.max((int) (ratio * n), n + 1);<a name="line.127"></a>
<FONT color="green">128</FONT>                oldt = t;<a name="line.128"></a>
<FONT color="green">129</FONT>                iterations.incrementCount();<a name="line.129"></a>
<FONT color="green">130</FONT>            }<a name="line.130"></a>
<FONT color="green">131</FONT>        }<a name="line.131"></a>
<FONT color="green">132</FONT>    <a name="line.132"></a>
<FONT color="green">133</FONT>        /**<a name="line.133"></a>
<FONT color="green">134</FONT>         * Compute the n-th stage integral.<a name="line.134"></a>
<FONT color="green">135</FONT>         *<a name="line.135"></a>
<FONT color="green">136</FONT>         * @param n Number of steps.<a name="line.136"></a>
<FONT color="green">137</FONT>         * @return the value of n-th stage integral.<a name="line.137"></a>
<FONT color="green">138</FONT>         * @throws TooManyEvaluationsException if the maximum number of evaluations<a name="line.138"></a>
<FONT color="green">139</FONT>         * is exceeded.<a name="line.139"></a>
<FONT color="green">140</FONT>         */<a name="line.140"></a>
<FONT color="green">141</FONT>        private double stage(final int n)<a name="line.141"></a>
<FONT color="green">142</FONT>            throws TooManyEvaluationsException {<a name="line.142"></a>
<FONT color="green">143</FONT>            // Function to be integrated is stored in the base class.<a name="line.143"></a>
<FONT color="green">144</FONT>            final UnivariateFunction f = new UnivariateFunction() {<a name="line.144"></a>
<FONT color="green">145</FONT>                    public double value(double x) {<a name="line.145"></a>
<FONT color="green">146</FONT>                        return computeObjectiveValue(x);<a name="line.146"></a>
<FONT color="green">147</FONT>                    }<a name="line.147"></a>
<FONT color="green">148</FONT>                };<a name="line.148"></a>
<FONT color="green">149</FONT>    <a name="line.149"></a>
<FONT color="green">150</FONT>            final double min = getMin();<a name="line.150"></a>
<FONT color="green">151</FONT>            final double max = getMax();<a name="line.151"></a>
<FONT color="green">152</FONT>            final double step = (max - min) / n;<a name="line.152"></a>
<FONT color="green">153</FONT>    <a name="line.153"></a>
<FONT color="green">154</FONT>            double sum = 0;<a name="line.154"></a>
<FONT color="green">155</FONT>            for (int i = 0; i &lt; n; i++) {<a name="line.155"></a>
<FONT color="green">156</FONT>                // Integrate over each sub-interval [a, b].<a name="line.156"></a>
<FONT color="green">157</FONT>                final double a = min + i * step;<a name="line.157"></a>
<FONT color="green">158</FONT>                final double b = a + step;<a name="line.158"></a>
<FONT color="green">159</FONT>                final GaussIntegrator g = FACTORY.legendreHighPrecision(numberOfPoints, a, b);<a name="line.159"></a>
<FONT color="green">160</FONT>                sum += g.integrate(f);<a name="line.160"></a>
<FONT color="green">161</FONT>            }<a name="line.161"></a>
<FONT color="green">162</FONT>    <a name="line.162"></a>
<FONT color="green">163</FONT>            return sum;<a name="line.163"></a>
<FONT color="green">164</FONT>        }<a name="line.164"></a>
<FONT color="green">165</FONT>    }<a name="line.165"></a>




























































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